Syst. Biol. 64(1):e42–e62, 2015
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DOI:10.1093/sysbio/syu048
Advance Access publication July 28, 2014
The Inference of Gene Trees with Species Trees
GERGELY J. SZÖLLŐSI1 , ERIC TANNIER2,3,4 , VINCENT DAUBIN2,3 , AND BASTIEN BOUSSAU2,3,∗
1 ELTE-MTA
“Lendület” Biophysics Research Group, Pázmány P. stny. 1A., 1117 Budapest, Hungary; 2 Laboratoire de Biométrie et Biologie
Evolutive, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 5558, Université Lyon 1, F-69622 Villeurbanne, France;
3 Université de Lyon, F-69000 Lyon, France; and 4 Institut National de Recherche en Informatique et en Automatique Rhône-Alpes, F-38334
Montbonnot, France;
∗ Correspondence to be sent to: Bastien Boussau, Laboratoire de Biométrie et Biologie Evolutive, Centre National de la Recherche Scientifique,
Unité Mixte de Recherche 5558, Université Lyon 1, F-69622 Villeurbanne, France; Université de Lyon, F-69000 Lyon, France;
E-mail: [email protected].
Received 30 October 2013; reviews returned 11 July 2014; accepted 14 July 2014
Associate Editor: Tanja Stadler
Abstract.—This article reviews the various models that have been used to describe the relationships between gene trees and
species trees. Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based
on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes
and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and
because alleles can coexist in populations for periods that may span several speciation events. Building models describing the
relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known,
and vice versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general
neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees.
These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several
types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along
the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree–species tree models
with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a more reliable
basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that
gene tree–species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of
genomic evolution. [Algorithm; amalgamation; Bayesian inference; birth–death model; coalescent; dynamic programming;
gene duplication; gene loss; gene transfer; gene tree; hybridization; maximum likelihood; phylogenetics; species tree.]
Toutes choses étant causées et causantes,
aidées et aidantes, médiates et immédiates, et
toutes s’entretenant par un lien naturel et
insensible qui lie les plus éloignées et les plus
différentes, je tiens impossible de connaître les
parties sans connaître le tout non plus que de
connaître le tout sans connaître particulièrement
les parties. (Pascal 1669).
During the last 50 years, phylogeny has become
more and more based on molecular data, increasingly
favoring homologous sequences over morphological
characters. This approach has been extremely fruitful,
producing constant improvement in the accuracy and
resolution of phylogenetic reconstruction together with
our understanding of evolutionary processes at the
molecular level. However, we have known all along that
we are barking up the wrong trees: with increasing
sophistication in the models of sequence evolution, we
have been reconstructing trees describing the history of
fragments of genomic sequence, which we will liberally
call “gene” in this review, but never the history of species.
Gene trees are not species trees (Maddison 1997).
Each gene tree reflects a unique story, which is linked
to species history, but often significantly differs from
it (Szöllősi and Daubin 2012). Gene trees reflect the
process of replication at a local level: a copy of a gene
at a locus in the genome, for example, a protein coding
gene, replicates and its copies are passed on from parent
to offspring, generating branching points in the gene
tree. Because each gene copy has a single ancestral copy,
barring recombination, all gene trees would be identical.
Recombination, however, breaks up the genomic history
into a series of partially independent stories, that is into
gene trees along the genomes of species.
Starting from an individual site in a genome up to
the species level, a hierarchy of evolutionary processes
generate genomic sequences. Individual sites evolve as
a result of point mutations. The fate of individuals
carrying each mutation is played out at the population
level, and determines whether a mutation is fixed in
the population as a substitution, or is ultimately lost.
The birth and death of stretches of sequence, e.g. of
single sites or even of entire genes, occurs as a result of
insertions and deletions in individual genomes, the fate
of which, similar to point mutations, is played out at the
population level. The source of the inserted sequence
differentiates between duplication events, wherein a
sequence from the same genome is inserted, and lateral
transfer events, wherein a sequence from an external
source is inserted. Finally, species, that is, populations
of genomes, evolve through speciation and extinction
events.
As illustrated in Figure 1 each level of the hierarchy
contributes to generating phylogenetic signal that can
lead to differences between reconstructed gene trees.
Segregating mutations that cross speciation events
(a process called incomplete lineage sorting) leave
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SZÖLLŐSI ET AL.—THE INFERENCE OF GENE TREES WITH SPECIES TREES
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FIGURE 1. A hierarchy of evolutionary processes contribute to sequence evolution. a) Individual species (circles) and their genomes evolve
among a population of species, according to a diversification process consisting of speciation (light gray, green online) and extinction (dark gray,
red online) events. The variation in the number of species existing at any given time is indicated by the dashed contour. When attempting to
infer the species tree typically only a fraction of existing species (gray and black circles on dashed line) are sampled (black circles). b) Inside each
genome, each gene evolves according to gene duplication, loss, and transfer events. c) Individual sites evolve through point mutations. Processes
at the gene and site level are played out at the population level, where changes fix or are lost.
topological signatures in gene trees (see Fig. 1c). Current
estimates indicate that up to 30% of the sequence of
the human genome is more closely related to Gorilla
than to Chimpanzee due to this process (Scally et al.
2012). Duplication, transfer, and loss events (Fig. 1b) lead
to large differences in both the size and phylogenetic
distribution of families of homologous genes, and at the
same time produce patent phylogenetic discord (Szöllősi
and Daubin 2012). Finally, the species diversification
processes influence lateral transfer, as most transfer
events come from donor species that have gone extinct
or have not been sampled (Szöllősi et al. 2013b).
When reconstructing a gene tree it is desirable
to integrate these different types of information in
order to maximize the amount of information used
and to insure the consistency of our prediction. In a
pioneering attempt to do so, Goodman et al. (1979)
proposed to reconstruct the history of a gene by
searching for the tree that minimizes the sum of
the number of nucleotide substitutions, duplications,
and losses. This parsimonious approach is clear and
conceptually straightforward, but it raises the difficulty
of determining the relative weights of events that
are very different in nature. However, if we can
construct a coherent and principled approach to
combine these events, it becomes possible to envisage
the reconstruction of a gene tree given a sequence
alignment and a known species tree (here we consider
sequence alignments, but unaligned sequences could
also be considered if a model of insertion–deletion is also
used to jointly infer the alignment and the gene tree).
Moreover, given a set of gene alignments, it would allow
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us to reconstruct the species history that has most likely
generated them. In a probabilistic framework, a model of
sequence evolution and a model of gene family evolution
accounting for duplication, loss, lateral transfer, and/or
incomplete lineage sorting can be combined using the
intuitive hypothesis of conditional independence (we
then obtain the “Felsenstein equation” Felsenstein 1988).
The probabilities of the two models can be multiplied
under the following two assumptions: (i) the species tree
is independent from the sequences conditional on the
gene tree, that is, if we are given the gene tree we do
not need additional information on the species tree to
compute the probability of the sequences and, (ii) if we
are given the gene tree we do not need the sequences to
compute the probability of a species tree.
In addition, parsimony approaches often generate a
large number of equivalent solutions and do not allow an
efficient exploration or integration over solution spaces.
Probabilistic models allow integrating or sampling over
the very large number of possible scenarios. For example,
it is possible to estimate the probability of a particular
gene tree, which is not only the probability of the
most likely scenario of sequence evolution and events
of gene duplication, transfer, and loss, but the sum of
the probabilities of all possible scenarios that could
have generated this tree given the species tree, and
the sum of the probabilities of all substitution histories
consistent with the gene tree that could have generated
the sequence alignment.
In the past 15 years, several such methods, which
model consistently the dependence between gene trees
and the species tree, have been developed and have
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shown improved accuracy for inferring both gene trees
and the species tree. In this review we present these
methods, explain the assumptions they make, introduce
how they work, and highlight some of the results
obtained with them. We focus on probabilistic models,
but discuss parsimony-based approaches in situations
where probabilistic models have not been developed
yet. We do not review methods that consider gene
count or gene presence/absence information, as they
altogether ignore sequence information once homology
relationships have been defined (some of these methods
do account for several processes however, for example,
gene duplication, transfer, and loss (Csuros et al. 2006)).
MODELING THE DEPENDENCE BETWEEN GENE TREE AND
SPECIES TREE
A gene family can contain genes from different species
at the same locus, or genes in a same genome at
different loci. The processes known to contribute to
gene family evolution include speciation and lineage
sorting (ILS if incomplete), gene duplication and loss
(DL), and gene transfer (T). Lineage sorting concerns
genes from different genomes at the same locus, whereas
duplications give rise to homologous genes on the
same genome at different loci. Transfers can insert
a gene at a new locus, or replace a homologous
gene at its locus. Hybridization can be seen as a
special type of transfer, affecting a large portion of
the genome, and resulting in a gene replacement
in the receiving species. Allopolyploidization is a
particular type of hybridization, in which the two
genomes keep cohabiting in subsequent generations. For
each individual process, there are published models
accounting for its effect, and recently some tend to
integrate several of them. So far, no model has been
published that deals with all processes together in a
coherent statistical framework.
Gene Birth–Death Generates Gene Trees
Along the Species Tree
Irrespective of whether they deal with ILS, DL, or
T, all models of gene family evolution can be seen
as generating a tree inside a tree, that is a gene
tree inside a species tree. In this respect, the models
encountered in the literature dealing with processes
of speciation and extinction (Rannala and Yang 1996;
Morlon et al. 2009) are very similar to the models of
gene family evolution. They both invoke birth–death
processes that generate a rooted, time-like tree topology.
Birth events correspond to bifurcations, death events
correspond to the loss of a lineage. In diversification
models, lineages correspond to species, in models
of gene family evolution they correspond to genes.
After the birth–death process arrives at the present,
lineages with no descendant among extant species are
usually pruned, and the remaining lineages constitute
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the generated tree topology. Models of gene family
evolution, however, are constrained by the species tree,
whereas species diversification models are not. The
species tree constitutes a set of constraints corresponding
to speciation events and branch lengths that control the
birth–death process generating the gene family tree. A
gene family evolution model is in essence a series of
birth–death models fitted piecewise along the branches
of a species tree (Fig. 2). The birth–death process
generating the gene tree starts above the root of the
species tree. Each time the birth–death process reaches
a speciation node, two new processes are created in the
children lineages. These processes can be identical, or
can have different parameters. In general, for n branches
in the species tree, counting the branch above the
root, there are n independent birth–death processes. Of
course, the parameters of these n independent processes
do not need to be independent: one can imagine that
the birth parameter for instance evolves according to for
example a Brownian motion process running along the
species tree. Such a model would penalize large jumps in
the birth parameter between neighboring branches of the
species tree, but to our knowledge such an idea has not
yet been implemented. Another source of dependence
between processes is lateral gene transfer: a birth in a
lineage may originate in another.
The above describes how a gene tree, complete with
branch lengths in units of time, is generated along the
clock-like branches of the species tree. In practice, to
simplify the problem, we will see that several methods
choose to consider only the topologies of gene trees,
that is the branch length information is discarded. In
this case, the mathematical machinery of the birth death
model is not used to compute the probability of a specific
dated scenario of observed birth and death events;
instead it is used to compute the probability of a given
succession of birth and death events (Degnan and Salter
2005; Wu 2011), or the probability of observing k genes at
the beginning of a branch of the species tree, and l genes
at the end of this same branch (Boussau et al. 2013). The
choice of discarding branch length information in the
gene tree in some cases simplifies the problem, because
fewer processes need to be modeled. Potentially useful
information, however, is discarded in the process.
The Coalescent Models Population-level Processes
Along the Species Tree
Coalescent models aimed at modeling the discordance
between gene tree and species tree arising from
population-level processes have enjoyed increasing
popularity in the last 10 years. Here birth events
correspond to the appearance of a new allele, and death
events to the disappearance of an allele, without any
change in the locus of the gene. At any given time in
a species, for a given locus in the genome, there may be
several alleles. These alleles have their own history, some
alleles being more closely related than others. When
speciation occurs, most alleles will be sorted randomly
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a)
SZÖLLŐSI ET AL.—THE INFERENCE OF GENE TREES WITH SPECIES TREES
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b)
FIGURE 2. Birth–death processes for generating species trees and gene trees. Death events (species extinctions and gene loss) are in dark gray
(red online), birth events (speciation, duplication and transfer events) are light gray (green online). a) Birth–death processes modeling speciation
and extinction. b) Birth–death process modeling gene family evolution inside a species tree.
between the two incipient species: in some cases both
species will receive copies of all alleles, in others, each
will receive only a subset of the alleles present in the
parent population. In all cases, the history reconstructed
from the allele sequences will be the allele history, and
not the species history. The allele history and the species
history always differ in the timing of the bifurcation
events: assuming no hybridization has occurred between
the lineages, alleles have necessarily split before species
split. They can also differ in their topology, especially if
only a brief interval of time passes between successive
speciation events, and/or the effective population size
of the parent species is large (Rosenberg and Nordborg
2002). Given the coalescent model, the amount of
discordance in topology and divergence times between
the trees of several loci and a species tree can therefore
be used to estimate effective population sizes along the
species tree (Rannala and Yang 2003; Liu and Pearl
2007; Heled and Drummond 2008; Minin et al. 2008;
Kubatko et al. 2009). Such a model where the population
size is assumed to differ between the branches of the
species tree has been called the multispecies coalescent
(Rannala and Yang 2003), and is now widely used to
infer species trees given several loci, with one allele per
locus (Liu and Pearl 2007; Heled and Drummond 2008;
Kubatko et al. 2009), or several alleles per locus (Liu
et al. 2008; Heled and Drummond 2010), using branch
lengths information in the gene trees (Liu and Pearl
2007; Heled and Drummond 2008), or instead relying
solely on their topologies (Degnan and Salter 2005; Wu
2011), in the maximum likelihood (Kubatko et al. 2009;
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Wu 2011) or Bayesian frameworks (Liu and Pearl 2007;
Heled and Drummond 2008; Liu et al. 2008; Heled and
Drummond 2010; Minin et al. 2008). Hey (2010) has
developed an extension of the multispecies coalescent
that allows migration between branches of the species
tree. The multispecies coalescent has also been used
in conjunction with a Hidden Markov Model (HMM)
running along a chromosome to infer recombination
rates, locus-specific trees, divergence times and effective
population sizes (Hobolth et al. 2007, 2011; Li and Durbin
2011; Mailund et al. 2011; Scally et al. 2012), given a
species tree and a genomic alignment. In this model, gene
trees can change along the alignment, and how often the
gene trees change provides information on the rate of
recombination.
One assumption of all the models we have presented
so far is that sequences are assigned to species without
ambiguity. However, for recently diverged populations,
it is often unclear whether two distinct populations
should be considered as coming from the same single
species, or should define two distinct species. In a given
sample, it can also be unclear how many species have
really been sampled. To address such cases, Rannala
and Yang have developed a model for delimiting species
given a set of sequences for different loci and several
individuals (Yang and Rannala 2010; Rannala and
Yang 2013). They assume a multispecies coalescent
model, and postulate that hybridization does not occur
after speciation. Information coming from for example
geographical distribution, morphology, or behavior can
be introduced into the model thanks to a prior on the
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SYSTEMATIC BIOLOGY
expected number of species, but also through a guide
tree, whose other purpose is to improve the efficiency
of the MCMC algorithm used for inference. Under
this model, they can analyze about 10 species for 100
sequences, with a finite number of loci. They apply this
method to well studied data sets of asexual rotifers and
fence lizards, and recover the species found by other
means.
Models of Gene Duplication and Loss
Models of gene duplication and loss usually ignore
population-level processes (but see Rasmussen and
Kellis (2012), discussed below) that drive the fixation
or disappearance of an allele, and only consider events
of gene duplication and loss that have fixed in the
species. In this setting, birth events correspond to fixed
gene duplications, and death events to fixed gene losses.
Probabilistic models for gene duplication and loss were
first proposed by Arvestad (2003), and further developed
in subsequent papers by the same group (Arvestad et al.
2004; Akerborg et al. 2009; Sjöstrand et al. 2012) and by a
few others (Dubb 2005; Rasmussen and Kellis 2007, 2010).
The focus of these works was to infer gene trees given a
fixed species tree, with clock-like branch lengths in units
of time, and with fixed rates of gene duplication and
gene loss over the entire tree. Combined with the birth–
death model of gene evolution is a hierarchical model
of the rate of sequence evolution, wherein the species
tree provides dates, and each gene family is associated
with one or several rates. Alternatively, Górecki et al.
(2011); Górecki and Eulenstein (2013) developed another
model for gene duplication, not based on a birth–death
process, but based on a Poisson process for computing
the probability of a parsimonious reconciliation of a gene
tree topology against a species tree. The gene tree does
not need to have branch lengths, but the species tree
does. For this reason, and because it does not include
a loss parameter, this model misses some of the realism
of the birth death processes described above, but gains
in speed.
More recently, we modified birth–death models to
allow different duplication/loss parameters for each
branch of a nondated species tree (Boussau et al. 2013).
To speed-up computations, we took an approach similar
to Górecki et al. (2011), and did not account for the
branch lengths of gene trees in their reconciliation with
the species tree. Instead we only reconciled topologies.
However, because our hierarchical model includes a
model of sequence evolution for joint inference of gene
trees and species tree, we still needed to estimate branch
lengths in the gene trees. To simplify the problem,
we chose not to have a hierarchical model of rates of
sequence evolution: rates for each gene family were
considered to be entirely independent. This decreased
the number of global parameters to estimate, but
increased drastically the number of gene family-specific
parameters to estimate.
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Models of Lateral Gene Transfer
Lateral gene transfer (LGT) corresponds to the
incorporation in a genome of a gene coming from a
different species. There is compelling evidence that this
process has played an important role in the evolution of
life, particularly in the domains of Bacteria and Archaea
(Abby et al. 2012). Several models have been proposed to
account for LGT in gene tree–species tree reconciliation.
So far they all consider events that have fixed and ignore
population-level processes. One key feature of these
models is whether they consider or not the possibility
of gene replacement. The recipient of a transfer may, or
may not have a gene homologous to the incoming gene in
its genome. If it has, the gene in the recipient can be either
conserved or lost. Transfer-only models usually consider
only gene replacement. Models that do not make this
assumption are often coupled with duplications and
therefore are presented in the subsequent section. The
difference between the two is important in that gene
replacement is not modeled by birth and death. Indeed,
replacing a lineage by a gene coming from another
breaks the independence assumption between lineages,
which is at the basis of efficient computations in birth–
death models. Thus, models of gene replacement differ
from the more mainstream birth–death models.
The first attempt at modeling probabilistically lateral
gene replacement explicitly was made by Suchard (2005),
but a model for host–parasite cophylogeny developed
by Huelsenbeck et al. (2000) could also be used to detect
gene transfer between two loci. This model assumed that
the parasite phylogeny differed from the host phylogeny
through a Poisson-distributed number of host-switches,
or replacements in our case. Transfer events could be
placed uniformly among branches, or preferentially
among branches close to each other in the host tree. Rates
of evolution were independent in the host tree and the
parasite tree, but sequence evolution was assumed to
follow a strict clock model. Inference was conducted in a
Bayesian framework employing MCMC, and resulted in
a host tree distribution, a parasite tree distribution, and
distributions of the number and rates of host switches.
Suchard (2005) proposed a model specifically
designed to tackle gene replacement on a gene tree
topology, discarding branch length information.
Computing the probability of a gene tree given a species
tree therefore did not involve mapping the gene tree
onto the species tree. Instead, this method involved
estimating how many Subtree Prune and Regraft (SPR)
moves (Hordijk and Gascuel 2005) were necessary to
explain the topological difference between a species
tree and a gene tree (another type of move was also
considered). The probability of a gene tree was then
based on this number of moves, through a Poisson
model. Using this model, Suchard (2005) could estimate
the species tree that best explained a forest of over
140 gene trees. However, the approach was limited to
trees with only 6–8 species because of its computational
cost. In addition, this approach does not make sure
that all transfers detected in a set of gene families
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are time-consistent: in principle a gene can only be
transferred to contemporaneous species, present in
the sample analyzed or not, and certainly not to more
ancient species. In Suchard (2005)’s approach, because
the species tree topology is not anchored in time,
time-consistent transfers and “back-to-the-future” type
transfers are not distinguished.
Bloomquist and Suchard (2010) chose another road
to modeling gene replacement, by drawing on models
of population genetics. They considered the Ancestral
Recombination Graph (ARG). An ARG is a type of
rooted network that combines both vertical and transfer
edges. Once an ARG is built, it can be used to generate
dated gene trees, which correspond to tree-like paths
obtained by selecting edges of the ARG. They aimed
at reconstructing an ARG that represents all of the
evolutionary histories of a set of distinct loci, some
of which evolved along the species tree, and some
of which underwent replacement events. They used
MCMC to propose ARGs, adding or subtracting transfer
edges through reversible jumps. Given an ARG, a gene
tree is drawn for each locus under study; these gene
trees can be totally independent of each other, or can
incorporate spatial information, so that two neighboring
genes on the genome are more likely to be transferred
together than distant genes. This allows modeling
different situations, such as single-gene conversion or
homologous recombination. In addition, the sequences
of different genes can evolve at different rates. In the end,
the method builds dated gene trees, and a dated ARG in
which vertices are annotated as vertical or transfer nodes,
and in which edges involved in a transfer event can be
annotated with the genes that are inferred to have been
transferred.
Models that Combine the Above
We know of five probabilistic models that combine
some of the processes listed above: the DTLSR model
a)
b)
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of Tofigh (2009), the DLCoal model of Rasmussen and
Kellis (2012), our ODT model (Szöllősi et al. 2012, 2013b),
network-based models of hybridization with incomplete
lineage sorting Than et al. (2007); Meng and Kubatko
(2009); Kubatko et al. (2009); Yu et al. (2012), and networkbased models of polyploidization (Jones et al. 2013).
Finally we discuss Bucky (Ane et al. 2007), a method
that does not assume any particular process to explain
the difference between gene tree and species tree but
instead clusters gene families according to how similar
their evolutionary history is.
The DLCoal model combines a coalescent model with
a model of gene duplication and loss. In doing so,
it reintroduces population genetics concepts into the
framework of DL models: for instance, it acknowledges
that a new duplicate first has a very low frequency
in a population, as it is present only in the individual
where the gene duplication occurred. Under this model,
the reconciliation of a gene tree with a species tree
requires three objects: first, a dated species tree, with
branches annotated with effective population sizes.
Second, a dated locus tree, generated thanks to a
birth–death process placing events of duplications and
losses along the species tree branches, according to a
duplication rate and a loss rate. The locus tree contains
implicit information about chromosomal positions, as
under this model chromosomal position changes at
duplication nodes, but is generated according to the
same birth–death process used in previous duplicationloss models (Arvestad 2003; Arvestad et al. 2004; Dubb
2005; Rasmussen and Kellis 2007; Akerborg et al. 2009;
Rasmussen and Kellis 2010; Sjöstrand et al. 2012).
Third, the gene tree (black trees in Fig. 3) is generated
according to a coalescent process running along the locus
tree (blue trees in Fig. 3). The DLCoal model makes
the simplifying assumption, termed the “hemiplasy
assumption”, wherein all duplications and losses are
considered to either always go extinct or never go extinct
in all descendant lineages. This assumption allows
c)
FIGURE 3. Duplication and loss events within a multispecies coalescent with the locus tree in gray (blue online) and the gene tree in black.
a) A duplication occurs in one chromosome and creates a new locus, locus 2 in the genome. At locus 2, the Wright–Fisher model dictates how
the frequency p of the daughter duplicate (black dots) competes with the null allele (white dots) until it eventually fixes (p = 1). A gene tree is
therefore a traceback in this combined process. b) A new duplicate can undergo hemiplasy, and fixes in some lineages and goes extinct in others.
c) Similar to duplication, a gene loss (deletion) starts in one chromosome and drifts until it fixes or goes extinct. Reproduced from Figure 1 in
Rasmussen M.D., and Kellis M., Genome Res. 2012;22:755–765.
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the separation of the duplication–loss process from
the multilocus coalescent. Aside of this assumption,
the model entails two successive tree-embedded birth–
death processes and can be regarded as a multispecies
colaescent process taking place along the locus tree
which in turn is generated along the species tree
by a DL process (cf. Fig. 3). Rasmussen and Kellis
(2012) implemented this model into a program that can
reconcile a gene tree with a species tree, given rates of
duplication and loss, a dated species tree, and effective
population sizes.
The DTLSR (Tofigh 2009; Tofigh et al. 2011; Sjöstrand
2013) and ODT models combine a model of gene
transfer with a model of gene duplication and loss.
Both are natural extensions of the DL models, and
do not employ an additional object like the locus
tree in the DLCoal model. Instead, the birth–death
process is modified to accommodate two types of birth
events, gene duplications and gene transfers. The ODT
model has been applied to biological datasets, and
has been extended to account for gene transfers that
involve species that have gone extinct or are otherwise
unrepresented in the tree under consideration (Szöllősi
et al. 2013b). In this extension of the ODT model, the
ex-ODT model, sampled species and their ancestors
are assumed to come from a population of species,
which at any given time contains many more species
than are present in the sample. This population of
species evolves according to the Moran process, but
could evolve according to more complex processes (e.g.,
(Morlon et al. 2009)). Within this framework, a gene
can be transferred from the genome of an ancestor
of a sampled species to the genome of a species
living at the same time, but which gave no descendant
among the sampled species. Then this gene can evolve
among the genomes of species that gave no sampled
descendant, including through transfers, duplications,
losses and speciations, and finally reintegrate genomes
with sampled descendants.
Contrary to the DLCoal model, neither the ODT
models or the DTLSR model account for populationlevel processes, and thus do not model allele fixation.
However, the two model types could be easily mixed, for
example the ex-ODT model could be used to generate a
locus tree, which would then be used to generate a gene
tree according to the coalescent model. This ex-DTLCoal
model would then account for speciations, extinctions,
duplications, losses, transfers, and incomplete lineage
sorting in a hierarchical probabilistic model (cf. Fig. 4).
Meng and Kubatko (2009); Kubatko et al. (2009);
Yu et al. (2012) propose a model for the detection of
hybridization in the presence of incomplete lineage
sorting, extending early efforts by Than et al. (2007).
As we noted above, from a modeling point of view,
hybridization may be seen as a high frequency of
gene replacements between two lineages. There, a
rooted phylogenetic network is used instead of a
phylogenetic tree. In a hybrid genome, any gene is
assumed to be coming from one of two parental
genomes. Hybridization nodes are thus represented in
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such a network by nodes with two parents A and B. A
probability indicates the proportion of genes coming
from parent A, the rest coming from parent B. Under
this model, evolution of alleles within the network is
very similar to their evolution along a species tree.
At nodes with a single parent, the usual multispecies
coalescent model applies, with the length of the branch
in coalescent units. At hybridization nodes, parent A
is chosen with probability , otherwise parent B is
chosen; then the usual multispecies coalescent applies
with the chosen parent. The model therefore does not
attempt to model the bottleneck that might occur during
hybridization. Yu et al. (2012), building upon Meng and
Kubatko (2009) who worked with a single hybridization
event, provide formulas for computing the likelihood of
a gene tree topology (without branch lengths) under this
model, for networks with any number of hybridization
nodes, which makes it possible in principle to carry
out gene tree inference or species tree inference. In
practice, they implemented this model in PhyloNet, so
that different candidate species trees or networks can
be compared according to their likelihood given a set
of gene tree topologies, or a set of gene tree topology
distributions. Kubatko et al. (2009) implemented an
algorithm to search for the optimal network according to
information criteria, with a model that considers branch
lengths in the gene trees in addition to their topologies.
In this implementation, the topology of the network
is fixed, and the object of inference is the presence
and number of hybridization nodes with the associated
parameters .
Allopolyploidization has also been modeled as a
specific case of hybridization (Jones et al. 2013). In this
context, allopolyploidization occurs when two diploid
individuals from different species mate, which results
in the birth of a viable new tetraploid species. Jones
et al. (2013) make the simplifying assumption that
there is no recombination between the alleles inside
the allopolyploid, and propose two models. In one
model, any number of allopolyploidization events can
be inferred, but evolution in the two genomes forming
the allopolyploid is assumed to be independent, which
disregards the fact that these genomes belong to the
same species. In the second model, only one event
of allopolyploidization can be inferred, but then the
evolution of the two genomes in the allopolyploid
is linked. In both cases, they use the multispecies
coalescent model to describe the evolution of alleles
along the species phylogeny or, in this case, the species
phylogenetic network. They apply these models to
simulated data sets as well as empirical data sets of less
than 10 species, less than 10 genes, and up to three alleles
per gene.
Another popular approach that deals with the variety
of gene tree histories is Bucky (Ane et al. 2007).
Bucky does not attempt to model the processes by
which gene trees differ from species trees. Instead, it
attempts to cluster gene families according to their
histories. Bucky needs families of orthologous genes,
which contain exactly 1 sequence per species. Once
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e49
FIGURE 4. Left: the hierarchy of sequence evolutionary processes plotted along two dimensions: sequence length, from single nucleotides
through genes to whole genomes; and time, from single generations through the neutral fixation time to large numbers of generations. Events
occurring in single individuals, such as point mutations, insertions/deletions etc. are filtered by the population-level process of selection and
drift with only a minority reaching eventual fixation. Speciation and extinction events affect entire genomes and require many generations.
Incomplete lineage sorting (blue online) occurs when fixation time overlaps with speciation time. Transfer events can cross large phylogenetic
distances and almost always involve evolution along extinct or unrepresented species and hence are affected by speciation dynamics. Right:
distribution of models discussed in the text based on the time and length scales of the evolutionary process they model. Classic molecular
phylogeny methods model only substitutions. DL models handle fixed duplication and loss events along with substitutions. The multispecies
coalescent and related methods model explicitly the fixation of point mutations (blue online). DLCoal models the fixation of both point mutations
and of gene-scale insertion/deletion events that lead to fixed duplication and loss events. DTL models (red online; ODT, DTLSR) extend DL
models to fixed transfer events, but ignore speciation dynamics. The ex-ODT model combines speciation dynamics with DTL events to provide
a more realistic model of transfer paths. A potential “ex-DTLCoal” model, as discussed in the main text would cover the area of all these models.
posterior distributions of phylogenetic trees have been
built from these families, Bucky attempts to cluster
the families by similarity of their evolutionary history.
This clustering is done in a nonparametric Bayesian
framework, which means that both the clustering and
the number of clusters are estimated from the data.
The end result may provide insight into the sources of
the heterogeneity among gene histories, for instance in
cases where neighboring genes are found to share the
same history. Additionally, Bucky has also often been
used to provide a candidate species tree, by gathering
clade frequencies from all gene histories. One strength of
Bucky is the fact that, provided orthology between genes
has been well defined, it does not depend on a particular
model of gene family evolution, and will work equally
well in the presence of transfers or incomplete lineage
sorting for instance. The corresponding drawback is that
it does not return direct estimates of the species tree, or
of rates of events such as duplications or transfers that
might be of interest to students of molecular evolution.
Simulation and Inference
One can see a phylogenetic pipeline as a series
of statistical inferences, starting from raw sequences
coming out of sequencing machines, and finishing
with the inference of a species tree (Fig. 5). Necessary
steps include sequencing error correction, assembly of
[14:13 8/12/2014 Sysbio-syu048.tex]
reads into contigs and scaffolds, gene annotation, gene
family clustering, alignment, and tree reconstruction.
Most of these steps are done sequentially, so that later
steps in the pipeline entirely disregard any estimate of
uncertainty from the previous steps, and do not provide
any feedback to these. Gene tree–species tree models take
a step toward a more principled approach, by allowing
communication between two steps of this pipeline, the
construction of gene trees, and the construction of a
species tree. Figure 5 places the above discussed models
and associated phylogenetic software in the context
of the complete phylogenetic inference pipeline. Gray
nodes are considered known, and white nodes are
inferred. This figure shows that a large diversity of
inferential problems have been addressed, considering
gene alignments, gene trees, species trees, or several
of these as data. In this section, we review some of
the methods and algorithms that have been used to
address these inferential problems. We do not discuss
methods aiming at reconstructing an alignment, and
instead focus on gene tree–species tree methods. As a
consequence, in the following we use “probability of an
alignment” loosely to describe the probability coming
from events of substitutions or jointly from events of
substitutions and insertion–deletions. We present how
data can be simulated, how the likelihood of a gene
tree or of a species tree can be computed efficiently,
and how good gene trees and species trees can be
searched for.
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VOL. 64
FIGURE 5. Gene tree–species tree models in the context of the phylogenomics inference pipeline. Left: the inference pipeline (some steps are
not represented, such as sequencing error correction). Right: graphical representation of the inferential problem for a selection of the models
and associated phylogenetic software discussed in the main text. The sequence of steps in the graphical model representations correspond to the
hierarchical sequence of evolutionary process generating genomic sequences (cf. Fig. 1). The likelihood that must be computed is also shown.
Graphical model conventions are observed: stochastic nodes, nodes corresponding to data considered as known are gray, and nodes whose
states are inferred are in white. The models have been simplified, and parameters others than the gene tree and the species tree have not been
represented.
Simulating gene trees.—Generating a simulated gene tree
according to a model is straightforward, and usually
involves traversing a species tree from its root to its leaves
(although simulation under the coalescent is done from
the leaves to the root). Assume there are k lineages at
time tbegin (which at first is the beginning of a branch)
on a branch i which ends at tend , with birth rate i
and death rate i . Two waiting times tbirth and tdeath
are randomly drawn from exponential distributions, one
with parameter k ∗i , and the other with parameter
k ∗i . If both are longer than tend −tbegin , no event
occurs along this branch. If tbirth is the shortest, then
a birth event occurs, and tbegin ← tbirth and k ← k +1.
If tdeath is the shortest, then a death event occurs, and
tbegin ← tdeath and k ← k −1. In both cases, the lineage
that has undergone the event is chosen uniformly. Then
the process starts again. Lineages found at the end of
a branch of the species tree are then given as input
to the next birth–death processes, running along the
descendant branches.
Lateral gene transfer can be regarded as simply
a peculiar birth event, one which results in the
birth of a gene copy in a branch of a species tree
different from the species tree branch of the ancestral
copy. Computationally, this introduces a dependency
between species tree branches, requiring that all
contemporaneous branches are considered together. To
simulate gene trees, one can then consider different
rates for different birth events, that is for duplications
and transfers Szöllősi et al. (2012). Alternatively, one
can consider replacement transfer, wherein, if a member
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of the homologous gene family is present in the
recipient genome, it is replaced by the transferred
gene. Computationally, this introduces a dependency
between gene tree branches that prevents the use of
algorithms that rely on the independence of gene
lineages (see below), but simulations can be carried
out in a straightforward manner (Galtier 2007). More
problematically, however, no simulation method has
been constructed to take into consideration the fact
that, in the presence of transfer, gene trees record
evolutionary paths along the complete species tree,
including extinct and unsampled branches, and not
only along the phylogeny of the species in which their
descendants reside today. This is the case because, as
first noted by (Maddison 1997) and later elaborated
by Zhaxybayeva and Gogarten (2004); Fournier et al.
(2009), although transfer events imply that the donor
and receiver lineages existed at the same time, the
donor lineage might have subsequently become extinct,
or more generally, might not have been sampled.
Brute force simulation of transfers along a “complete
phylogeny” are expensive due to the large number of
species that must be considered. There are at least
two possible alternatives: (i) use instead parametric
bootstrap-like methods described below or (ii) use
approximations. One such approximation could be
based on the assumption that the number of species
represented in the species tree is much smaller that the
total number of species Szöllősi et al. (2013b), similar to
the assumptions of the coalescent.
A parametric bootstrap-like approach was used by
(Szöllősi et al. 2013b) in the context of the ALE+ex-ODT
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model (ALE standing for Amalgamated Likelihood
Estimation) to produce simulated alignments based on a
species tree and real alignments from 36 cyanobacteria.
The approach consisted of first reconstructing the most
probable gene trees according to the joint likelihood
associated with duplication, transfer and loss rates given
a fixed species tree and the gene family alignments.
Second, the inferred gene trees were then used to
simulate alignments. Third, these alignments were fed
back into ALE+ex-ODT to assess its reconstruction
accuracy, comparing both the reconstructed gene trees
and the associated duplication, transfer and loss events
to those used in the simulation. This approach has
the advantage of circumventing potentially complex
simulations while at the same time retaining otherwise
hard to reproduce properties of biological datasets, such
as the distribution of gene family sizes and the variation
of evolutionary rates within and among gene families
Szöllősi and Daubin (2012).
Computing the conditional probability of a gene tree.—By the
joint conditional probability of a gene tree, we mean the
probability of a gene tree given a gene alignment and a
species tree. There are (at least) two components to the
conditional probability of a gene tree. One component
corresponds to the model of sequence evolution running
along the gene tree; the other to the model of gene
family evolution running along the species tree. In both
cases, dynamic programming algorithms traversing the
nodes of gene trees and species trees can often efficiently
compute the relevant component of the probability.
Along a branch of a tree of a given length (the
gene tree for sequence-based models or the species
trees for gene family evolution models), probabilities of
descendant states given ancestral states are computed
by solving differential equations similar to other birth–
death processes (for some processes, the solution can
be obtained analytically, in others, numerical integration
is necessary). Dynamic programming is then used to
traverse branches of the tree in postorder. That is,
branches are considered starting from their leaves up
to the root. If a tree is unrooted, and all nodes need
to be considered as potential roots, nodes need to be
visited three times (although only two tree traversals
are necessary, (Guindon and Gascuel 2003; Boussau and
Gouy 2006)), according to the three possible directions
for the root.
The probability of an alignment given a gene tree
is computed along the gene tree alone, whereas the
probability of a gene tree given a species tree is computed
along both the gene tree and the species tree. In both
cases, at a leaf, data can be used to fill a vector of
probabilities. For sequence evolution, data correspond to
the state found at the site under consideration (e.g., A, C,
G, or T in a DNA sequence). For the model of gene family
evolution, this corresponds to the presence, absence, or
number of genes found in a given extant species. Then, at
internal nodes, probability distribution vectors from the
children nodes are used to compute the probability of a
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given subtree, according to the process considered in the
branches. At the root, dynamic programming algorithms
yield a probability for the entire tree.
The rough description above outlines the algorithm
developed by Felsenstein (1981) to compute the
probability of a multiple alignment of gene sequences
given a gene tree and a model of sequence evolution. In
this case, the differential equations corresponding to the
Markovian process of sequence evolution can be solved
analytically to obtain substitution probabilities along a
branch of a given length. Computing the probability of a
gene tree given a species tree is a bit more complicated,
as it involves mapping the gene tree onto the species
tree to compute the probability of presence of a gene
tree node or branch at each node or branch of the
species tree. This mapping is natural at the leaves: a
gene from species A is mapped onto leaf A of the
species tree. For internal nodes, the mapping can be
helped by the consideration of node ages in models that
consider that both the gene trees and the species tree
are dated. This is typically the case with multispecies
coalescent models (e.g., Rannala and Yang 2003). Such
a method yields a single mapping between the nodes
of a given gene tree and a given species tree, for given
rates of sequence evolution. In a duplication and loss
context, Akerborg et al. (2009) improved upon this
approach by analytically integrating over the possible
mappings as well as over rates of sequence evolution,
again through dynamic programming. Their approach
requires “slicing” the species tree by dropping extra
nodes along the branches of the tree. These two methods
yielding either a single mapping or integrating over all
mappings in the context of dated trees have counterparts
in the context of nondated trees. On one hand, Boussau
et al. (2013) assumed the most parsimonious mapping
between the nodes of the gene tree and the nodes of
the species tree. This most parsimonious mapping is
obtained with a single tree traversal (Zmasek and Eddy
2001). On the other hand, Szöllősi et al. (2012) took a
similar approach to Akerborg et al. (2009) by integrating
over all the possible mappings between the nodes of the
gene tree and the nodes of the species tree, again through
dynamic programming, but without considering dated
gene trees. This allowed them to avoid using a model of
rate evolution. However, it was necessary to order the
nodes of the species tree, which has the effect of slicing
it and adding new nodes, for correctly computing the
probability of a gene tree given a species tree. As this
inference includes transfer in addition to duplication
and loss, numerical integration is necessary to solve the
differential equations describing the birth and death
process because gene lineages mapping to different
branches of the species tree are dependent and no
analytical solutions are available.
Usually such algorithms can achieve linear complexity
in the number of genes for coalescent or DL models,
but modeling transfers raises the complexity to the
product between the number of nodes in the gene tree
and the number of nodes in the species tree. Methods
that require slicing the species tree (Akerborg et al.
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2009; Tofigh 2009; Doyon et al. 2010; Szöllősi et al. 2012)
introduce new nodes in the species tree and therefore
are more expensive. However, in models with transfers,
slicing the species tree is necessary as computing the
probability of a gene tree given a species tree is provably
difficult when the species tree nodes are not ordered,
except if time-inconsistent transfers are allowed (Tofigh
et al. 2011). It is also costly to model gene transfers
that occur by replacing existing genes (like in SPR-like
events of (Suchard 2005; Nakhleh et al. 2005; Beiko and
Hamilton 2006; Bloomquist and Suchard 2010; Abby
et al. 2012)). Indeed, this replacement introduces a
dependency between separate gene tree lineages, which
prevents the use of dynamic programming algorithms.
In this context, the space of gene trees must be explored
using SPR-like moves to compute the probability of a
gene tree given a species tree. Note that current methods
that slice the species tree (Tofigh et al. 2011; Szöllősi
et al. 2012, 2013b) explicitly handle gene replacement
transfers, but can only account for such events as a
transfer event followed immediately by a loss in the
receiving lineage.
For models of sequence evolution as well as models of
gene family evolution, the same dynamic programming
scheme can be used to make a variety of inferences.
If we focus on models of gene family evolution, this
scheme can be used to obtain a maximum parsimony
reconciliation or the reconciliation that maximizes the
probability of the gene tree given the species tree,
to integrate over all reconciliations to compute the
probability of a gene tree given a species tree, or
to sample among reconciliations according to their
probability. For a survey on available algorithms and
software for reconciliations as of 3 years ago see (Doyon
et al. 2011).
Combining the probability of a gene alignment given
a gene tree with the probability of the gene tree given a
species tree can be achieved by the multiplication of the
two probabilities (Maddison 1997; Akerborg et al. 2009;
Szöllősi et al. 2013b), assuming that the gene alignment
is independent of the species tree conditional on the
gene tree. The same assumption is at the heart of the
model by Rasmussen and Kellis (2012) who combine
probabilities from a multispecies coalescent model and
a DL model, through the addition of an additional layer,
the locus tree (see section “Modeling the dependence
between gene tree and species tree”). Thanks to two
conditional independence assumptions, the probability
of the entire structure is obtained by the product of three
probabilities.
Computing the probability of a gene tree given
a phylogenetic network according to a multispecies
coalescent model, as in Yu et al. (2012), requires
specific algorithms in addition to usual ones, and the
introduction of a new type of tree, the MUL tree.
The MUL tree is a multilabeled tree generated from a
phylogenetic network as follows: every hybridization
node with its two parents A and B is removed from
the tree, then duplicated, and finally one copy is
attached to A and the other to B. The MUL tree
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therefore contains several copies of subtrees coming
from hybridization nodes, but it is no longer a network,
as all nodes have a single parent; the computation of the
probability of a gene tree then involves usual dynamic
programming algorithms running along the MUL tree,
with three complications. The first is that all possible
mappings of the alleles to the duplicated subtrees must
be considered—this creates a combinatorial factor that
can substantially increase computing time. The second
is that the multispecies coalescent process must be
aware of the number of alleles evolving in a duplicated
subtree when computing the propagation probability of
an allele. The third is that the hybridization probabilities
must be taken into account (see the “Modeling the
dependence between gene tree and species tree” section
for more details about ) to compute the probability of
an allele trajectory along the MUL tree. MUL trees are
also used by Jones et al. (2013), as an intermediate step
to compute the probability of a phylogenetic network
in their most accurate model that can handle a single
allopolyploidization event, and as object of inference in
their more flexible but less faithful model.
Finding good gene trees.—If we do not assume gene trees
to be known, exploring the space of possible gene trees is
usually achieved, similar to sequence evolution models,
by either hill climbing maximum likelihood strategies
(Vilella et al. 2008; Thomas 2010; Rasmussen and Kellis
2012; Boussau et al. 2013; Wu et al. 2013), or stochastic
sampling of trees using Markov Chain Monte Carlo
(MCMC) algorithms (Liu and Pearl 2007; Heled and
Drummond 2008; Minin et al. 2008; Akerborg et al. 2009;
Heled and Drummond 2010; Rasmussen and Kellis 2010).
These local searches are inspired by classic gene tree
search algorithms (Guindon and Gascuel 2003), and
the MCMC or hill climbing steps use, for example,
random NNI (nearest neighbour interchanges) or SPR
(subtree prune and regraft) moves. As such searches
can be computationally intensive, SPRs are sometimes
bounded (Boussau et al. 2013), or rearrangements are
directed (Szöllősi et al. 2012). Devising good directed
rearrangements is sometimes called gene tree correction,
and entails for example decreasing the number of
duplications in a duplication/loss most parsimonious
reconciliation: such moves have some chance to increase
the probability of a gene tree according to the model
of gene family evolution. If at the same time they do
not decrease the likelihood according to the model of
sequence evolution by a large portion, such moves are
accepted (Chang and Eulenstein 2006; Muffato et al. 2010;
Chaudhary et al. 2012; Lafond et al. 2013). Reconciliations
with polytomies in a gene tree (Lafond et al. 2012) can
also be used to correct or construct good gene trees
according to a sequence model and a species tree.
An alternative to local search in gene tree space is the
amalgamation of reconciled gene trees from a sample
of trees (David and Alm 2011; Szöllősi et al. 2013a).
As illustrated in Figure 6 this approach consists in
combining clades found in a sample of gene trees based
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FIGURE 6. Based on gene trees sampled according to their posterior probability, conditional clade probabilities (CCP) can used to estimate
the posterior probability of any tree that can be amalgamated (Höhna and Drummond 2012) from clades present in the sample. Conditional clade
frequencies can be used to approximate CCPs and are computed as the fraction of times a particular split of a clade, for example (abc,de) is
observed among all trees in which the containing clade, for example (abcde) is found. Estimates based on the sample of trees on the left are
shown as fractions for two different gene trees that can be amalgamated. The estimate for a gene tree is given by the product of the frequencies.
Amalgamated likelihood estimation (ALE (Szöllősi et al. 2013a)) is a probabilistic approach to exhaustively explore all reconciled gene trees that
can be amalgamated as a combination of clades observed in a sample of gene trees. Based on the sample on the left, the tree with the highest
posterior probability is the third tree (blue online). Reconciling it with the species tree requires 1 transfer and 1 loss event. It is, however, possible
to combine clades present in the second (green online) and third (blue online) trees to produce a gene tree that is not present in the original
sample but is identical to the species tree, that is it requires 0 events to draw it into the species tree. Depending on the relative probabilities of
P(0 events) and P(1 transfer and 1 loss), the joint conditional probability may prefer the scenario without transfer.
on a model of sequence evolution (e.g., sampled using
MCMC) in order to find the optimal gene tree according
to both the model of sequence evolution and the model
of gene family evolution. The probabilistic application
of this method relies on the observation (Höhna and
Drummond 2012; Larget 2013; Szöllősi et al. 2013a) that it
is possible to efficiently and accurately approximate the
probability of an alignment for a very large number of
gene trees using conditional clade frequencies based on
a much smaller sample of trees. Combined with a model
of gene family evolution, this allows the construction of
a gene tree that maximizes the product of the probability
of the alignment given the gene tree and the probability
of the gene tree given the species tree, or alternatively
to sample reconciled gene trees according to the joint
conditional probability (Szöllősi et al. 2013a). Here also
a dynamic programming algorithm is used and the
computation of a gene tree that maximizes the joint
conditional probability is polynomial in the number of
trees in the sample, which can be much faster than a local
exploration, and can also be used as a starting point for
local exploration.
Finding a good species tree.—One can also assume
that the species tree is unknown, and search for it.
Indeed integrative models of evolution should be able
to retrieve the information about species evolution
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from the alignment better than averaging methods like
concatenations or supertrees.
If we assume independence between genes, much
like we usually assume independence between sites
in most models of sequence evolution, a score for a
species tree can be computed by adding (in parsimony)
or multiplying (in probabilistic contexts) the joint
conditional probabilities (scores in parsimony) for all
gene trees. Optimization algorithms can then be used
to search for the species tree with the best overall score
or probability.
Methods for species tree inference under coalescent
models (minimizing the number of ILS events or
maximizing a joint conditional probability for a set of
gene trees) are reviewed by Liu et al. (2009) and can be
found on the online resource STRAW (Shaw et al. 2013).
Fast approximations are given by distance or supertree
methods (Than and Nakhleh 2009; Liu et al. 2010; Liu and
Yu 2011; Yu et al. 2013), whereas Bayesian sampling is
more precise but computationally intensive (Heled and
Drummond 2010; Liu et al. 2008; Kubatko et al. 2009).
In a duplication and loss framework, Wehe et al. (2008);
Bansal et al. (2010); Chaudhary et al. (2010) use the total
number of duplications and losses as a global score and
propose an efficient way to perform SPR (subtree prune
and regraft) and tree bisection reconnection (TBR) moves
on one candidate species tree to decrease the score. These
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heuristics perform SPRs in a specific order, so that only
a small portion of the mapping between gene trees and
species trees needs to be recomputed, hence resulting in
significant savings in computing time.
Alternatives to local searches are the search for
exact solutions (Chang et al. 2011), or, inspired
by coalescent models, supertree methods resembling
the amalgamation of gene trees mentioned in the
previous section, which seem to quickly provide good
approximations of parsimonious species trees (Bayzid
et al. 2013).
Considering transfers in a probabilistic framework,
Szöllősi et al. (2012) explored time-ordered species trees,
that is, species trees in which internal nodes are totally
ordered. Topology search was performed by a directed
local search guided by apparent highways of transfers:
rearrangements are proposed in parts of the species tree
that show the highest numbers of transfers in the hope
of proposing rearrangements that reduce phylogenetic
discord.
All of the above methods take as their input fixed gene
trees. However, as we have several times recalled, good
gene trees computed with the help of the (correct) species
tree are substantially more accurate. Joint estimation has
been achieved by Heled and Drummond (2010); Boussau
et al. (2013), but with a very high computational cost.
Improvements in the algorithms used would be very
welcome.
IMPACT ON SYSTEMATICS AND GENOME EVOLUTION
The methods we described in the previous sections
have shown repeatedly that they improve on methods
that do not model gene family evolution for problems as
diverse as species tree estimation, gene tree estimation,
and the study of genomic evolution. In this section, we
present some of their most salient results.
Learning about Species Relationships and History
Coalescent models have been used extensively to
investigate species trees (e.g., (Alström et al. 2011; Gray
et al. 2011; Reid et al. 2012; Rocha et al. 2013)), because
contrary to supertree or concatenation methods they
should be robust against incomplete lineage sorting
effects (Degnan and Rosenberg 2006). However, methods
that jointly infer gene and species trees remain limited
in their ability to handle large data sets: they cannot
handle more than a few dozen species, and a few dozen
loci. In their place, approximate methods have had to be
used on genomic-scale data sets. As these take gene trees
as input, they require much less computer resources,
but suffer from the propagation of errors made during
gene tree inference. Song et al. (2012) used MP-EST
to reconstruct a well-resolved mammalian species tree
based on 447 genes from 37 species. They found that the
traditional technique, which consists of concatenating
the alignments for several loci, was significantly less
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consistent when run on subsets of the data than MPEST. However, another study by McCormack et al. (2013)
found a highly unresolved tree when they used the same
program on a data set of 416 Ultra Conserved Elements
(UCEs) form 32 species of birds. They assumed that the
small size of the UCEs led to unresolved and erroneous
gene trees, which in turn caused MP-EST to estimate
a highly unresolved species tree. This illustrates that
methods that do not infer gene trees, but rather obtain
them from external sources are by construction very
sensitive to the quality of the input gene trees, and calls
for more accurate and robust methods able to jointly infer
gene and species trees in the coalescent framework, for
large data sets.
Models of gene duplication and loss, or of gene
transfer, have also been used to reconstruct species
trees, although more sparingly than coalescent-based
models. The construction of a species tree given many
fixed gene trees has been performed many times under
a parsimony DL framework, searching for the species
tree that minimizes the total number of duplications
or duplications and losses. In that context, phylogenies
have been proposed for many clades (Slowinski et al.
1997; Page and Cotton 2002; Cotton and Page 2003;
Than et al. 2008). Genome-wide scale was reached by
Burleigh et al. (2011) who propose a plant phylogeny
with 18,896 gene trees. So far, these models have mostly
provided species phylogenies that were consistent with
the literature (Suchard 2005; Szöllősi et al. 2012; Boussau
et al. 2013). However, perhaps one of the most surprising
benefits of modeling gene family evolution comes
from modeling lateral gene transfer. Gene transfer is
often described as a mere nuisance, which prevents
phylogeneticists from obtaining well-resolved and easyto-interpret species trees. According to this viewpoint,
modeling gene transfer is useful because it provides
a principled way to discriminate between vertical
descent and lateral transfer: lateral transfers can then
be discarded to focus on vertical descent and obtain a
species phylogeny. However, gene transfer also provides
additional information about ancestral species and their
history.
For example, David and Alm (2011) infer the gene
birth rate along a deep phylogeny of prokaryotes,
and conclude that 25% of the genes in their data set
were born in the Archean. They used a dated tree
to infer transfers. But transfers can help date species
trees, because gene transfers can only occur among
contemporaneous species, and then be inherited by
descendant species. A pattern of gene transfers therefore
orients a species tree, from ancestral species that gave
genes but did not receive many, to more recent ancestors
that received genes from more ancient species.
Based on this idea, we ordered speciation events in
Cyanobacteria using 8332 genes in 36 species (Szöllősi
et al. 2012). We found that the information provided by
transfer events supported a root different from the root
obtained using outgroup species. However, outgroup
sequences are usually very distant from Cyanobacteria,
and the choice of the outgroup species affects the rooting
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of the tree. In addition, we find that support for our
unusual root comes from more than 200 transfer events.
Overall, the information gained thanks to the use of a
model of gene family evolution provides a new light
into the order of speciation events in Cyanobacteria. It
also provides a unique insight into genomic evolution
in this clade, by providing an accurate reconstruction
of ancestral gene contents. Because the ODT model
infers events of gene transfers, duplications and losses,
the number of genes present in ancestral genomes in
each gene family is a natural outcome. Future analyses
of ancestral gene contents based on models like ODT
should provide windows into ancient metabolisms and
phenotypes.
Another important process shaping species
relationships is hybridization. Models that aim at
inferring hybridization in the presence of incomplete
lineage sorting have been used in several systems and
have often found cases of hybrid speciations. Meng and
Kubatko (2009) studied four genes in four species of
cicadas from New Zealand to support an hypothesized
hybrid origin for one species. Yu et al. (2012) and
Bloomquist and Suchard (2010), using a Maximum
Likelihood and a Bayesian approach, investigated 106
genes from yeast species (6 in Bloomquist and Suchard
(2010), 5 in Yu et al. (2012)) and agreed about their
inference of hybridization ancestral to two species. In
addition, Bloomquist and Suchard (2010) studied 9
gene regions in spirochaete Bacteria, and confirmed
previous results that one horizontal gene transfer
happened in the history of these genes. Thanks to
their integrative Bayesian method, they were able to
date this event. Finally, Yu et al. (2012) studied more
than 9000 genes in three Drosophila genomes and also
detected hybridization ancestral to one of the three
species, this time in disagreement with Pollard et al.
(2006), whose analysis concluded that incomplete
lineage sorting was enough to explain the pattern of
incongruence in these genomes. Overall, these results
show that network-based methods are powerful and can
detect past hybridization events. Only Bloomquist and
Suchard (2010)’s method can infer the network topology,
but the other methods can be run on a set of topologies
to compare their likelihoods.
Improving Gene Tree Reconstruction and Learning about
Genome Evolution
Beyond species tree reconstruction, coalescent models
have also been used to investigate genomic evolution in
closely related species. For instance, a method based on a
Hidden Markov Model was used to estimate divergence
times, effective population sizes and recombination rates
in several species of primates. Insights include weaker
selection operating on the X chromosome than expected
(Hobolth et al. 2007), evidence for selection operating on
genes (Hobolth et al. 2011), and a negative correlation
between chromosome size and chromosome-specific
ancestral effective population size (Mailund et al. 2011).
The latter correlation is indicative of the power of
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recombination to increase effective population size:
because, at each meiosis, each chromosome undergoes
at least one recombination event, there are more
recombination events per base on small chromosomes,
which then increases the effective population sizes on
small chromosomes.
The use of a species tree in addition to a gene
alignment yields better gene trees than methods that
only consider the gene alignment. Akerborg et al. (2009)
studied a dataset of about 180 gene families in 17
yeast genomes with two methods, their own method
that uses the sequence alignment and a species tree,
and mrBayes, that only uses the alignment (Ronquist
et al. 2012). Several of these yeast species descend
from a species whose genome has been duplicated.
As a consequence, all gene trees in the data set must
show a duplication event in the branch containing this
species. They found that their method detects a branch
corresponding to a whole genome duplication in 66%
of the gene families, when mrBayes only detects this
branch in 35% of the cases. Rasmussen and Kellis (2010)
obtained a similar result by comparing the inferred
orthologs from gene trees obtained using 11 methods
to orthologs inferred from synteny information, on a
data set of 16 fungi. The seven methods that use the
information provided by the species tree were found to
outperform the four methods that only use the sequence
alignments, agreeing with synteny in about 90% of the
cases versus 60%, respectively. Other tests based on a
measure of tree balance after a duplication, or based
on simulated data all concurred that the information
provided by the species tree and interpreted by DL
models greatly improves phylogenetic reconstruction.
More recently Mahmudi et al. (2013) sample gene trees
and reconciliations in an MCMC framework under
a DL model and infer duplication and loss rates on
a vertebrate tree. Their conclusion is not only that
sequence-based trees are often wrong, but also that
most parsimonious reconciliations of good gene trees
are often improbable. Reconciled gene trees have also
been used to detect paralogs that originate from whole
genome duplications in teleosts (Ouangraoua et al.
2011; Howe et al. 2013) or at the base of vertebrates
(Makino and McLysaght 2010; Affeldt et al. 2013)
and understand the causes of their maintenance or
detect the current traces of these duplications and
reconstruct ancestral genomes. They have also been
used to study the evolution of metabolism in fungi
(Eastwood et al. 2011; Floudas et al. 2012). These
authors study fungi that digest wood: brown-rot fungi,
which digest only cellulose, and white-rot fungi, which
digest both cellulose and lignin, the most resistant
component in wood. Focusing on a subset of enzymes,
and reconciling their gene trees with the species tree,
they find that brown-rot fungi are derived white-rot
fungi that have lost several important genes. They also
infer that white-rot fungi appeared concomitantly with
the disappearance of coal deposits, and suggest that
lignin decay pathways in white-rot fungi may have
caused this disappearance.
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SYSTEMATIC BIOLOGY
FIGURE 7. Left: species tree inferred by PHYLDOG, with ancestral genome contents reconstructed by different methods on selected nodes.
Ancestral genomes reconstructed by PHYLDOG, in blue, have a size similar to that of extant genomes. Right: reconstruction of ancestral gene
neighborhoods. Two genes are considered neighbors if there is no other gene between them in the dataset, so in a linear chromosome every
gene (except two) should have two neighboring genes. So we expect from a method to recover exactly two neighbors for most ancestral genes.
PHYLDOG is in blue. Figure reprinted with permission from Boussau et al. (2013).
Although gene tree reconstruction benefits from the
input of an accurate species tree, it can probably suffer
from the use of an erroneous species tree. Unfortunately,
especially as new genomes get sequenced, accurate and
well-resolved species trees are not always available. To
address such situations and jointly infer the species
tree and gene trees, we developed PHYLDOG (Boussau
et al. 2013) and Fig. 7. We tested this program on both
simulated and real data and found that both the species
tree and the gene trees were reconstructed with good
accuracy. Notably, as with the methods that use a given
species tree to reconstruct gene trees, we found that our
method improved upon methods that only use sequence
alignments as input.
From a statistical point of view, joint reconstruction
of the species tree and gene trees is the most principled
approach, but it is computationally very challenging. In
Szöllősi et al. (2013a), we used an approach that is almost
as accurate as methods that explicitly infer gene trees
while being easier to put in practice. We considered as
our data a distribution of gene trees for each gene family
instead of just a single gene tree. Using the ALE dynamic
programming algorithm (see section “Simulation and
inference”), this approach provides a fast but accurate
approximation of the actual amount of phylogenetic
information contained in the sequence alignment. We
found that by not using a single gene tree as our data,
the estimates of the number of gene transfers in the
Cyanobacterial data set were 60% lower than when a
single gene tree was used. This suggests that the claim
that there have been too many transfers in Bacteria and
Archaea for reconstructing the tree of life may have been
a premature exaggeration. Szöllősi et al. (2013a) provides
a method to reconstruct a gene tree given a species tree
[14:13 8/12/2014 Sysbio-syu048.tex]
and rates of duplication, transfer, and loss, which can be
given or all be inferred provided enough information
is given to the program. Simulations and measures
based on reconstructed ancestral genomes show that
these gene trees are more accurate, but the biological
relevance of how improved these trees are is perhaps best
shown by ancestral sequence reconstruction. Groussin et
al. (submitted) reconstructed sequences based on trees
inferred through the Szöllősi et al. (2013a) approach,
which uses the species tree and a distribution of
gene trees, or through PhyML (Guindon et al. 2010),
an accurate method that does not take the species
tree into account. On simulations, this comparison
showed that the ancestral sequences were much more
accurate when based on the trees obtained with the
help of the species tree. More strikingly, the in vitro
resurrection of a protein belonging to the ancestor of
Firmicutes, an ancient group of Bacteria, showed that
the protein reconstructed based on the method using
the species tree was thermodynamically more stable
than the protein reconstructed from the alignmentonly tree, and exhibited better enzymatic capabilities.
As ancestral sequence resurrection is a popular and
powerful approach (Gaucher et al. 2003; Thomson et al.
2005; Gaucher et al. 2008; Bridgham et al. 2009; PerezJimenez et al. 2011; Finnigan et al. 2012; Harms and
Thornton 2013), methods using a model of gene family
evolution could make an important contribution toward
a better understanding of molecular evolution.
FUTURE CHALLENGES
Methodological issues are still numerous and leave
open wide research avenues, while at the same time the
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e57
potential of already available methods can be exploited
on an increasingly large scale.
coalescent gene tree-species tree models is still an open
question.
Bypassing the Gene Tree in the Multispecies Coalescent
The multispecies coalescent model describes the
evolution of polymorphisms along a species phylogeny.
Computing the likelihood of a gene alignment using
this model requires summing over a large space of
gene trees, given a species tree. This computational
difficulty is a major hurdle to using this approach on
large data sets, containing large numbers of species, and
large numbers of gene families. Very recently, Bryant
et al. (2012) and De Maio et al. (2013) came up with
two elegant approaches to computing the likelihood
of an alignment under the multispecies coalescent,
by bypassing entirely the gene tree level, and instead
analytically integrating over the space of possible allele
histories. These models present the first methods to
explicitly carry out the integral in the Felsenstein
equation (Felsenstein 1988; Hey and Nielsen 2007).
Bryant et al. (2012) consider biallelic data, and provide
a model and an algorithm, called SNAPP, that can be
used to reconstruct a species tree given an alignment
of single nucleotide polymorphisms for instance. They
develop a specific algorithm to address the fact that
the coalescent process fundamentally functions from the
tips of the species tree to its root, whereas the mutation
process works forwards. They use this algorithm to
reconstruct species trees with 69 individuals in 6 species
of Digitalis plants. De Maio et al. (2013) instead propose
a model for sequence data with A,C,G,T data by
using a substitution matrix over a larger state space
than the usual 4×4 substitution matrices: it contains
all 6 biallelic states {A,C}, {A,G}... with a range of
frequencies. They focus on a specific model, where they
consider a range of 10 possible frequencies per biallelic
frequencies: for the state {A,C}, we therefore have the
states {A10%,C90%}, {A20%,C80%}, ..., {A90%,C10%}.
Two assumptions are made: first, no more than 2 alleles
at a given site can be found at any time in a population,
and second their frequencies are well approximated
by the limited range included in the model. They
construct transitions between states of this matrix from
a population size parameter, selection coefficients, and
mutation rates. The resulting instantaneous rate matrix
is then exponentiated to provide a matrix of substitution
probabilities. Overall, the matrix obtained with a range
of 10 possible frequencies per biallelic state contains 58
states, that is about the same number of states as a codon
substitution model. De Maio et al. (2013) use this model,
with some further refinements to account for contextdependent mutations and strand-specificity on a large
alignment of four species of primates and find evidence
for a smaller ancestral population size in orangutans, and
selection on splicing enhancers in exons.
Such analytical approaches seem very promising for
combining coalescent models with duplication, loss and
transfer models, as they bypass the problem of sampling
allele histories. How they improve upon multispecies
More Integrative Models
The integrative program of Goodman et al. (1979)
is being progressively implemented. The probabilistic
framework makes it possible to integrate sequence
mutations with gene duplications and losses through the
coalescent (Rasmussen and Kellis 2012), or to integrate
duplications, losses, and transfers with substitutions
(Szöllősi et al. 2012; Boussau et al. 2013; Szöllősi
et al. 2013a,b). Rearrangements can be handled using
parsimony if ILS is ignored (Bérard et al. 2012; Patterson
et al. 2013).
A model and method to handle a union of all of these
processes is currently missing. However, there are very
good reasons for the integration of different levels of data
analysis to continue. For instance, below the gene tree /
species tree problem, is the inference of gene alignments.
Only recently has the problem of joint inference of
alignments and gene trees been considered seriously,
with attempts to model the process of insertion/deletion
in the evolution of sequences. Such approaches show
dramatic improvements over phylogenetically unaware
alignment methods (Redelings and Suchard 2005; Satija
et al. 2009; Warnow 2013). However, they obviously need
all the information necessary to have the best possible
gene tree, for example a link to the species tree. Hence,
it is probable that the integration of gene tree–species
tree models and alignment methods should benefit the
inference of alignments, gene trees and perhaps species
trees.
Although a global model seems difficult to imagine
presently, the entire pipeline of sequence data analysis,
from sequencing error corrections to gene annotation
and genome assembly is likely to benefit from
probabilistic evolutionary models. The recognition of
homologous sequences, the prediction of gene functions
based on information from other organisms, and
the proximity of genes on chromosomes all depend
ultimately on the structure of the species tree and
the possible events of substitution, duplication, loss,
and lateral transfer that may have occurred in the
history of genomes. There is currently no proposition
of an integration of these processes on all levels of
the pipeline described in Figure 5, but phylogenetically
aware methods have proved very promising at many
different steps of the process (Boussau and Daubin 2010)
including on genome assembly (Husemann and Stoye
2010; Rajaraman et al. 2013).
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Algorithmics and Computing Time
The score of a gene tree, especially if it is the
combination of scores from several models, can be fairly
costly to compute. Therefore, the exploration of trees
is always time consuming. Already the inference of a
gene tree that maximizes the probability of the alignment
given the gene tree is provably hard. The joint inference,
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VOL. 64
FIGURE 8. Evolutionary units below or above genes. Individual units (red and blue online) can be inside genes or genes that are neighbors along
a chromosome or genes involved in a protein complex. Adjacencies are binary relations between genes, and evolve along a species phylogeny.
Adjacencies can be gained or lost regardless of the birth and death of the units. When two units together undergo speciation, duplication, or
transfer, adjacencies undergo the same events.
estimation of parameters, and exploration of dated or
ordered species trees combine intractable problems. In
practice, optimizing a gene tree can necessitate up to
a few hours for very large families. As there can be
thousands of gene families in a typical dataset, the
computations even for a fixed species tree can take a
long time. However, models of gene family evolution as
well as sequence-based models all make the assumption
that genes evolve independently from each other. This
assumption can be questioned (see below) and is also
broken by evolutionary parameters shared among gene
families. But it allows a trivial parallelization by the data.
All genes trees can be computed independently, given a
common species tree. Hence, a species tree exploration
is mainly constrained by the largest multigene families.
A simple way to increase computational efficiency is to
ignore these large families in a first step of species tree
exploration. Large multigene families can be considered
later, when a good species tree is found based on
smaller gene families, or, in a sampling context, using
importance sampling. However, such tricks can only
help as long as the number of genomes under study
is relatively small. For studying larger datasets, we will
need to devise more efficient algorithms.
Reconstructing and Dating the Tree of Life
A confusion between gene trees and species trees is
arguably at the origin of the claim that Darwin was
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wrong when he evoked the image of a tree of life,
because he failed to foresee the role of lateral gene
transfer in microbial evolution (Doolittle 1999). The
models and methods described above actually show that
the plurality of gene histories can not only be overcome
but more importantly provides additional information
on the processes and patterns of species evolution.
The phylogenies for a diversity of clades have been
reconstructed with coalescent, DL or DTL models. In
each case, the degree of conflict among gene trees can
be interpreted in biological terms, such as divergence
time and ancestral population size with the coalescent,
or relative timing of speciation with LGT. There is a
great hope that the development and use of these models
will help resolve many issues that were left pending by
traditional methods.
Beyond the Gene as an Evolutionary Unit
Although we have adopted a liberal sense for “gene”,
in many of the studies we reported, a gene is a sequence
coding for a protein or a functional RNA, and is
considered as an evolutionary unit. However, within
such genes, different parts may have different histories
(Didelot et al. 2010; Wu et al. 2012). Alternatively,
some genes may be associated throughout evolutionary
times because their functions are interdependent or
simply because they are close to each others in the
genome. As such, they may be duplicated or transferred
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together (Bansal et al. 2013; Patterson et al. 2013).
Hence, the definition of evolutionary units is difficult,
and fluctuates in time (Fig. 8). As we have shown,
almost all existing models describe the reconciliation
of one gene tree with one species tree, supposing its
evolution is coherent and independent from other genes.
Some genomic studies, however, allow genome-wide
parameters like the rates of duplications and losses
to vary across branches of the species tree (Boussau
et al. 2013). This can be seen as a trick to model
large-scale events like genome duplications without
doing away with the independence of genes, which
is computationally advantageous. But it fails to model
more local rearrangements such as duplications of parts
of a chromosome. These events could be informative for
phylogeny, but models of genome rearrangements are
often combinatorially so complex (Fertin et al. 2009) that
they do not scale up well with the size and number of
genomes (York et al. 2002; Darling et al. 2008; Miklós and
Tannier 2010). Until now, their complexity has precluded
a coupling with other models such as gene tree–species
tree reconciliation. However, assuming neighborhoods
between genes are independent, meaning that for any 3
genes A, B, C the neighborhood between genes A and B
is independent of whether genes A and C are neighbors
or not, it is possible to integrate rearrangements into
DL (Bérard et al. 2012) or DTL (Patterson et al. 2013)
models. Such approaches describe the evolution of
neighborhoods (or any other relationship between genes,
including functional ones) along pairs of reconciled gene
trees, allowing one to reconstruct adjacencies in ancestral
genomes and evolutionary events of duplication, loss,
and transfer that have affected genomic fragments
comprising several genes. Because such multiple events
are frequent, it is likely that the parameters of
duplication, transfer, and loss that are estimated in DL
and DTL models are biased and it seems necessary
to integrate models of neighborhood evolution with
phylogenetic reconstruction into the reconstruction of
genome histories.
There are also models for detecting breakpoints inside
gene sequences using HMMs for instance (McGuire et al.
2000; Suchard et al. 2002; Martins et al. 2008; Boussau
et al. 2009), or detecting breakpoints of phylogenetic
discordance at a whole genome scale (Ané 2011), but so
far these models have not been included in models of
gene family evolution.
Keeping Up with the Pace of Data Acquisition
Currently, genome sequencing is no longer a limiting
step for comparative genomics. Instead, assembling gene
families, gene alignments, gene trees, and a species
tree are becoming increasingly problematic. In this
context, methods using models of gene family evolution
may offer an advantage because they effectively reduce
the space of possible solutions to explore: given a
species tree, the space of possible gene trees is limited
compared with species tree unaware methods, and
consequently, so is the space of possible alignments.
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Devising smart algorithms that make use of these
reductions of complexity may provide fast yet accurate
inferences for large-scale comparative genomics projects.
Another area where progress is needed is in the
reuse of prior information. Currently, every time a new
comparative genomics project is undertaken, or every
time a database of homologous sequences is updated,
many inference tasks need to be redone from scratch.
The computations of gene families, alignments, trees,
and species tree are usually done as if there was no
prior information obtained from previous analyses. This
is obviously a huge waste of useful information, as
these computations are often very demanding. Future
approaches to comparative genomics will need to be not
only integrative, but also incremental. There is a clear
need for new developments, and the Systematic Biology
community is well equipped to undertake them.
CONCLUSION
In the past 15 years, the relationship between gene
trees and the species tree has been greatly clarified.
This conceptual advance has been accompanied by
methodological developments in models of gene family
evolution and in the algorithms needed for statistical
inference. These rely heavily on coalescent and birth–
death processes and dynamic programming. In the next
few years, these developments will go two seemingly
incompatible ways: they will have to increase in
complexity to more accurately model genome evolution,
but they will also need to scale up as the sizes of
data sets keep increasing. This tension presents exciting
challenges.
FUNDING
This project was supported by the French Agence
Nationale de la Recherche (ANR) through Grant ANR10-BINF-01-01 “Ancestrome.” G.J.S. was supported by
the Marie Curie CIG 618438 “Genestory” and the Albert
Szent-Györgyi Call-Home Researcher Scholarship A1SZGYA-FOK-13-0005 supported by the European Union
and the State of Hungary, co-financed by the European
Social Fund in the framework of TÁMOP 4.2.4. A/1-111-2012-0001 “National Excellence Program.”
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